In this paper, we study robust large-scale distributed learning in the presence of saddle points in non-convex loss functions. We consider the Byzantine setting where some worker machines may have abnormal or even arbitrary and adversarial behavior. We argue that in the Byzantine setting, optimizing a non-convex function and escaping saddle points become much more challenging, even when robust gradient estimators are used. We develop ByzantinePGD, a robust and communication-efficient algorithm that can provably escape saddle points and converge to approximate local minimizers. The iteration complexity of our algorithm in the Byzantine setting matches that of standard gradient descent in the usual setting. We further provide three robust aggregation subroutines that can be used in ByzantinePGD, including median, trimmed mean, and iterative filtering. We characterize their performance in statistical settings, and argue for their near-optimality in different regimes including the high dimensional setting.

该研究探讨了在Byzantine设置下使用鞍点来最小化非凸损失函数的鲁棒分布式学习算法，提出了一种名为ByzantinePGD的算法来逃脱鞍点并收敛到真实局部最小值，通过三种鲁棒梯度估计器的性能特征，论证了它们在低维和高维时的近最优性。

抵御拜占庭容错分布式学习的鞍点攻击